Asteroid shapes: From LASPA to Current Ideas

Alberto Cellino, Carlo Comito, Paolo Tanga, Paolo Paolicchi, Daniel Hestroffer, Derek Richardson, Aldo Dell’Oro

During the decade between 1980 and 1990, a lot of work was done in asteroid science, and

the three guys below were very active

All this led to realize that Collisions have been a major evolutionary process for the asteroid main belt

population

(ℓ is given in units of )

Data from Poznan catalog, (maintained by A. Kryszczynska)

Available shape estimates do not fit very well... Because asteroids are certainly not perfectly fluid bodies

The basic ideaA gravitational aggregate will tend to minimize its Energy

E = Egrav + Erot

if it is not at equilibrium, it will evolve its shape and spin in order to keep the Energy to the minimum possible value, being given the total angular momentum of the system.

The simple assumption is that, for a given Angular Momentum, the overall rearrangement of the configuration will be driven by the gradient of Energy.

We start from a variety of possible initial shapes, andwe look at how they evolve, for different values of A.M.

Using PKDGRAV (developed by D.C. Richardson)

Bodies are modeled as sets of equal-size, smooth (no surface friction) spheres held together by gravity

1.Start with a dispersed cloud of spherules, and allow them to collapse to a spherical assemblage under their own gravity.

2.Carve from this assemblage a set of triaxial ellipsoids having different axial ratios, each formed by about 1,000 spherules.

3.Apply a rigid rotation to reach a given amount of (adimensional) Angular Momentum, to characterize in this way a set of different initial conditions.

4.Run PKDGRAV and follow the evolution of each system.

Set of initial shapes

The heritage of Paolo: Gravitational aggregates

Stable quasi-equilibrium shapes, not identical to theoretical equilibrium shapes for fluid bodies.

For increasing A.M., the flattening tends to increase.

Trend to reach b/a ≈ c/a in many cases

Compatible with friction angles (angles of repose) less than 10°

Compatible with observed distribution of shapes of relatively large asteroids.